The origin of the magnetic field in clusters of galaxies is unclear. It has been suggested that the field is the result of dynamo action acting on a small seed field (Jaffe 1980; Roland 1981; Ruzmaikin, Sokoloff & Shukurov 1989). Recent detailed models (Goldman & Rephaeli 1991; De Young 1992) show that this model is inadequate - the field that can be generated in this process is an order of magnitude weaker than actually observed. Furthermore, Goldschmidt & Rephaeli (1993) showed that the Faraday Rotation data could not be explained by the turbulent dynamo model, primarily due to the very low filling factor caused by the ropelike structure of the field (Ruzmaikin et al. 1989).
In a recent paper I argued that radio haloes were formed in cluster mergers (Tribble 1993), the turbulence and shocks induced by the merger accelerating relativistic electrons to the energies where they can radiate at the observed frequencies. I pointed out that a source of relativistic electrons and magnetic fields was needed. I there suggested that old relic radio galaxies were the source of both the fields and particles. The lifetimes of the relativistic particles and the magnetic field are rather different: the particles lose energy rapidly (by synchrotron and inverse Compton processes), while the field is frozen into the plasma and decays very slowly. Thus any magnetic field that is injected into the intracluster medium remains there and is built up over the lifetime of the cluster. In this paper I follow this point further and calculate the expected field strength in the intracluster medium.
I first begin by describing the radio source population in galaxy clusters, and then present some examples to show that the potential for magnetization of the intracluster medium by powerful radio sources is very large. I then integrate over the radio luminosity function and over the age of a cluster to get the accumulated magnetic energy density today. I briefly discuss the mechanism whereby the field is dispersed into the intracluster medium before presenting my conclusions.